ellipsePoints function

Compute Radially Equispaced Points on Ellipse

Compute points on (the boundary of) an ellipse which is given by elementary geometric parameters.

ellipsePoints(a, b, alpha = 0, loc = c(0, 0), n = 201, keep.ab.order=FALSE)

Arguments

• a,b: length of half axes in (x,y) direction. Note that $(a,b)$ is equivalent to $(b,a)$ unless

  keep.ab.order=TRUE.

• alpha: angle (in degrees) giving the orientation of the ellipse, i.e., the original (x,y)-axis ellipse is rotated by angle.

• loc: center (LOCation) of the ellipse.

• n: number of points to generate.

• keep.ab.order: logical indicating if $(a,b)$ should be considered ordered. When FALSE, as per default, the orientation of the ellipse is solely determined by alpha.

  Note that keep.ab.order = TRUE seems a more natural default, but FALSE is there for back-compatibility.

Returns

A numeric matrix of dimension n x 2, each row containing the (x,y) coordinates of a point.

Author(s)

Martin Maechler, March 2002.

See Also

the list("ellipse") package and ellipsoidhull

and ellipsoidPoints

in the list("cluster") package.

Examples

## Simple Ellipse, centered at (0,0), x-/y- axis parallel:
ep <- ellipsePoints(5,2)
str(ep)
plot(ep, type="n",asp=1) ; polygon(ep, col = 2)
## (a,b) = (2,5)  is equivalent to (5,2) :
lines(ellipsePoints(2,5), lwd=2, lty=3)
## keep.order=TRUE : Now, (2,5) are axes in x- respective y- direction:
lines(ellipsePoints(2,5, keep.ab.order=TRUE), col="blue")

## rotate by 30 degrees :
plot(ellipsePoints(5,2, alpha = 30), asp=1)
abline(h=0,v=0,col="gray")
abline(a=0,b= tan( 30 *pi/180), col=2, lty = 2)
abline(a=0,b= tan(120 *pi/180), col=3, lty = 2)

## NB: use x11(type = "Xlib") for the following if you can
if(dev.interactive(TRUE)) {
  ## Movie : rotating ellipse  :
  nTurns <- 4 # #{full 360 deg turns}
  for(al in 1:(nTurns*360)) {
      ep <- ellipsePoints(3,6, alpha=al, loc = c(5,2))
      plot(ep,type="l",xlim=c(-1,11),ylim=c(-4,8),
           asp=1, axes = FALSE, xlab="", ylab="")
  }

  ## Movie : rotating _filled_ ellipse {less nice to look at}
  for(al in 1:180) {
      ep <- ellipsePoints(3,6, alpha=al, loc = c(5,2))
      plot(ep,type="n",xlim=c(-1,11),ylim=c(-4,8),
           asp=1, axes = FALSE, xlab="", ylab="")
      polygon(ep,col=2,border=3,lwd=2.5)
  }
}# only if interactive